Necessary and sufficient conditions for existence of maximal solutions for inf-α composite fuzzy relational equations

Authors:
Yu-mei Li;Xue-ping Wang
Affiliations:
School of Information Engineering, Beijing Technology and Business University, Beijing 100037, People's Republic of China;Department of Mathematics, Sichuan Normal University, Chengdu, Sichuan 610066, People's Republic of China
Venue:
Computers & Mathematics with Applications
Year:
2008

Citing 4
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Abstract

On complete Brouwerian lattices, an inf-@a composite fuzzy relational equation and its equation system are investigated. In finite domains, a necessary and sufficient solvability condition is proposed for the equation, then all its maximal solutions and the whole solution set are determined. Subsequently, the whole solution set for the equation system is determined. In infinite domains, sufficient conditions for existence of a maximal solution for the equation and the equation system are shown, respectively. Afterwards, a necessary and sufficient condition, that there exists a maximal solution which is more than or equal to any solution, is presented for the equation.